Simpy after gathering enough hero shards you can promote any characters star level to the next level by clicking the promote button and paying credits and shards.
You can obtain hero shards via:
– Rewards for completing Operations in Operations Mode
– Rewards for completing Heroic Campaign missions
– Buying character shards in the Arena Store with Arena Medals
– Rewards for completing weekend Challenges in Challenge Mode
– Rewards for completing Achievements
– Buying Basic Chests with power credits or Hero Chests with power gems in the Store
– Buying hero shards in the Store

On each characters card description it tells you where you can obtain their related hero shards from.

How To Get Unlimited Free Injustice Power Credits/Coins Without Hacks – Working Glitch 3/22/17 → https://www.youtube.com/watch?v=i1KrhfOVJV0